Results 1 to 2 of 2

Thread: Please solve my question

  1. #1
    stevengoh911
    Guest

    Please solve my question

    Given
    x,y ∈ [0,2c]
    f(x),g(y) ∈ [0,2c]
    Show
    | xy-f(x)-g(y)|≥ c≤
    exist

    I don't really get this question.
    Please help me
    Last edited by ThePerfectHacker; Jul 10th 2007 at 09:38 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by stevengoh911 View Post
    Given
    x,y ∈ [0,2c]
    f(x),g(y) ∈ [0,2c]
    Show
    | xy-f(x)-g(y)|≥ c≤
    exist
    It is assumed that $\displaystyle c>0$:

    Consider the points $\displaystyle (0,2c),(2c,0),(0,0)$ if these work then we are finished. Otherwise,
    $\displaystyle |f(0)+g(0)|<c^2$
    $\displaystyle |f(2c)+g(0)|<c^2$
    $\displaystyle |f(0)+g(2c)|<c^2$

    Now, the claim is that $\displaystyle |f(2c)+g(2c)-4c^2|\geq c^2$.
    This is true because,
    $\displaystyle f(2c)+g(2c) = [f(2c)+g(0)] + [f(0)+g(2c)] - [f(0)+g(0)] < c^2+c^2+c^2 = 3c^2$
    But then,
    $\displaystyle f(2c)+g(2c) - (2c)(2c) < 3c^2 - (2c)(2c) = -c^2$
    Thus,
    $\displaystyle |f(2c)+g(2c) - (2c)(2c)|\leq c^2$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to solve this question with a ti-89
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Mar 6th 2012, 11:31 AM
  2. how should i solve this question?
    Posted in the Algebra Forum
    Replies: 9
    Last Post: Mar 4th 2012, 07:33 PM
  3. I'm not sure how to solve this question?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 18th 2010, 09:14 AM
  4. How I can solve this question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Dec 24th 2009, 01:55 AM
  5. How should I solve this question?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Oct 18th 2006, 10:11 AM

Search Tags


/mathhelpforum @mathhelpforum